Erratum: Probing the stability of the spin-liquid phases in the Kitaev-Heisenberg model using tensor network algorithms [Phys. Rev. B<b>90</b>, 195102 (2014)]

Iregui, Juan Osorio; Corboz, Philippe; Troyer, Matthias

doi:10.1103/physrevb.90.239903

Cited by 7 publications

(17 citation statements)

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“…2 (for the iDMRG simulations we keep χ = 1200 states), which agrees with previous studies 4, [21][22][23][24][25] . For this L 2 , the system is compatible with the sublattice transformation that maps zigzag to AF and stripy to FM 22 .…”

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confidence: 77%

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Dynamics of the Kitaev-Heisenberg Model

Gohlke¹,

Verresen²,

Moessner³

et al. 2017

Phys. Rev. Lett.

136

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We introduce a matrix-product state based method to efficiently obtain dynamical response functions for two-dimensional microscopic Hamiltonians, which we apply to different phases of the Kitaev-Heisenberg model. We find significant broad high energy features beyond spin-wave theory even in the ordered phases proximate to spin liquids. This includes the phase with zig-zag order of the type observed in α-RuCl3, where we find high energy features like those seen in inelastic neutron scattering experiments. Our results provide an example of a natural path for proximate spin liquid features to arise at high energies above a conventionally ordered state, as the diffuse remnants of spin-wave bands intersect to yield a broad peak at the Brillouin zone center.Introduction. The interplay of strong interactions and quantum fluctuations in spin systems can give rise to new and exciting physics. A prominent example are quantum spin liquids (QSL), as fascinating as they are hard to detect: they lack local order parameters and are instead characterized in terms of emergent gauge fields. On the experimental side, spectroscopic measurements provide particularly useful insights into such systems, in particular by probing the fractionalised excitations (e.g. deconfined spinons) accompanying the gauge field. Such measurements can be related to dynamical response functions, e.g. inelastic neutron scattering to the dynamical structure factor. On the theoretical side, determining the ground state properties of such quantum spin models is already a hard problem, and it is even more challenging to understand the dynamics of local excitations.Here we present a combination of the density-matrix renormalization (DMRG) ground state method and a matrix-product states (MPS) based dynamical algorithm to obtain the response functions for generic twodimensional spin systems. With this we are able to access the dynamics of exotic phases that can occur in frustrated systems. Moreover it is also very useful for regular ordered phases where one would conventionally use large-S approximations, which in some cases cannot qualitatively explain certain high energy features 1,2 . We demonstrate our method by applying it to the currently much-studied Kitaev-Heisenberg model (KHM) model on the honeycomb lattice

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supporting

confidence: 77%

“…The gapped ground state having a non-zero flux through the cylinder overestimates the stability of the QSL phases. It is notable how well the phase boundaries agree with those from the infinite projected entangled pair state (iPEPS) simulations 21 .…”

supporting

confidence: 61%

Dynamics of the Kitaev-Heisenberg Model

Gohlke¹,

Verresen²,

Moessner³

et al. 2017

Phys. Rev. Lett.

136

View full text Add to dashboard Cite

show abstract

“…Based on 24-site ED calculation, Yamaji et al pointed out that a lattice expansion from Na 2 IrO 3 may stabilize a Kitaevtype spin-liquid state 18 . Since it was already shown that the iPEPS is able to describe the Kitaev spin liquid state reliably 21 , searching and designing the spin liquid state by using the combined DMRG or PEPS on the realistic and first-principles framework is an intriguing future subject.…”

Section: Discussionmentioning

confidence: 99%

“…Note that the iPEPS has been able to describe the Kitaev spin liquid state by using the full update optimization if it is applied to the Kitaev-Heisenberg model 21 . Therefore, the method is capable of describing the Kitaev spin liquid in general.…”

Section: Appendix B: Ipeps Calculation Methodsmentioning

confidence: 99%

“…Applicability of the newly developed TN method to ab initio Hamiltonians containing complex interactions beyond simple model Hamiltonians 21 , is examined by carefully comparing with the ED and DMRG. If the trigonal distortion is close to that of the ab initio Hamiltonian for Na 2 IrO 3 , the two methods show the zigzag order consistently with the exact diagonalization results in Ref.…”

Section: Introductionmentioning

confidence: 99%

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Ground-state properties of Na2IrO3 determined from an ab initio Hamiltonian and its extensions containing Kitaev and extended Heisenberg interactions

et al. 2017

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We investigate the ground state properties of Na2IrO3 based on numerical calculations of the recently proposed ab initio Hamiltonian represented by Kitaev and extended Heisenberg interactions. To overcome the limitation posed by small tractable system sizes in the exact diagonalization study employed in a previous study (Yamaji et al., Phys. Rev. Lett. 113, 107201 (2014)), we apply two-dimensional density matrix renomalization group, and infinite-size tensor-network method. By calculating at much larger system sizes, we critically test the validity of the exact diagonalization results. The results consistently indicate that the ground state of Na2IrO3 is a magnetically ordered state with zigzag configuration in agreement with experimental observations and the previous diagonalization study. Applications of the two independent methods in addition to the exact diagonalization study further uncover a consistent and rich phase diagram near the zigzag phase beyond the accessibility of the exact diagonalization. For example, in the parameter space away from the ab initio value of Na2IrO3 controlled by the trigonal distortion, we find three phases: (i) an ordered phase with the magnetic moment aligned mutually in 120 degrees orientation on every third hexagon, (ii) a magnetically ordered phase with a 16-site unit-cell, and (iii) an ordered phase with presumably incommensurate periodicity of the moment. It suggests that potentially rich magnetic structures may appear in A2IrO3 compounds for A other than Na. The present results also serve to establish the accuracy of the first-principles approach in reproducing the available experimental results thereby further contribute to find a route to realize the Kitaev spin liquid.

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Heisenberg–Kitaev physics in magnetic fields

Janssen

Vojta

2019

J. Phys.: Condens. Matter

136

104

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Magnetic insulators in the regime of strong spin-orbit coupling exhibit intriguing behaviors in external magnetic fields, reflecting the frustrated nature of their effective interactions.We review the recent advances in understanding the field responses of materials that are described by models with strongly bond-dependent spin exchange interactions, such as Kitaev's celebrated honeycomb model and its extensions. We discuss the field-induced phases and the complex magnetization processes found in these theories and compare with experimental results in the layered Mott insulators α-RuCl 3 and Na 2 IrO 3 , which are believed to realize this fascinating physics.

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Erratum: Probing the stability of the spin-liquid phases in the Kitaev-Heisenberg model using tensor network algorithms [Phys. Rev. B90, 195102 (2014)]

Cited by 7 publications

References 0 publications

Dynamics of the Kitaev-Heisenberg Model

Dynamics of the Kitaev-Heisenberg Model

Ground-state properties of Na2IrO3 determined from an ab initio Hamiltonian and its extensions containing Kitaev and extended Heisenberg interactions

Heisenberg–Kitaev physics in magnetic fields

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